integral of xsin(-4x)

Lösung

\int x sin (- 4 x) d x

\frac{1}{4} x cos (4 x) - \frac{1}{16} sin (4 x) + C

Schritte zur Lösung

\int x sin (- 4 x) d x

Wende die partielle Integration an

= - \int - 2 x^{2} cos (4 x) d x - \frac{1}{2} x^{2} sin (4 x)

\int - 2 x^{2} cos (4 x) d x = - \frac{1}{16} (8 x^{2} sin (4 x) - sin (4 x) + 4 x cos (4 x))

= - (- \frac{1}{16} (8 x^{2} sin (4 x) - sin (4 x) + 4 x cos (4 x))) - \frac{1}{2} x^{2} sin (4 x)

Vereinfache

- (- \frac{1}{16} (8 x^{2} sin (4 x) - sin (4 x) + 4 x cos (4 x))) - \frac{1}{2} x^{2} sin (4 x) : \frac{1}{4} x cos (4 x) - \frac{1}{16} sin (4 x)

= \frac{1}{4} x cos (4 x) - \frac{1}{16} sin (4 x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} x cos (4 x) - \frac{1}{16} sin (4 x) + C

\int \frac{1}{( x ^{2} + 25 ) ^{\frac{3}{2}}} d x

(4 x - y) d x + (6 y - x) d y = 0

\int (5 x^{2} - 6)^{\frac{3}{2}} d x

\frac{d}{d x} (\frac{12}{ln ( x )})

\int \frac{8 t ^{3} - 3 t ^{2} + 8 t}{t ^{2} + 1} d t